Angular correlation between two slow electrons in a Coulomb field

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Diagonalisation of the Coulomb interaction between two equivalent electrons in a degenerate hydrogenic manifold leads to tight confinement of the lowest eigenvector to the region theta 12 approximately= pi , where theta 12 is the angle between the two radius vectors. Both exact diagonalisation and alternative models based on O4 group symmetry are shown to lead to a Gaussian distribution in pi - theta 12 with a full width at half maximum given by theta 0n-1/2 for large principal quantum number n. Values of theta 0 are presented and compared with analogous results from Wannier and alternative theories for the escape of two slow electrons once the threshold n to infinity is reached. An analytical expression is obtained in this limit, with theta 0=135'. Although all the results share the same scaling dependence on n-or, equivalently, on the energy E-Wannier theory is uniquely different, particularly in the dependence of theta 0 on the charge Z of the positive ion. The precise origin of this uniqueness is traced to the non-adiabatic coupling between radial and angular motion that is crucial to Wannier theory.

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Journal of Physics B: Atomic, Molecular and Optical Physics

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